Quantum measurement of the electromagnetic field amplitude and phase by optical homodyning

The possibility of measuring the amplitude and phase of the electromagnetic field by optical light homodyning is shown. A new method for determining the relative phase of the field using the interference scheme of balanced homodyne detection is proposed. The method is based on direct measurement of the average complex amplitude of a quantum field mixed with a classical field using a passive symmetric beam splitter under conditions of a balanced homodyne measurement scheme. A “direct” measurement of the average field amplitude is a direct measurement of the real and imaginary parts of the average quantum mechanical value of the complex field amplitude by homodyning. By comparison with the quantum theory of the Hermitian phase operator of the electromagnetic field, the accuracy of this measurement is estimated for various quantum states of the microscopic electromagnetic field.